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A backbone is a subset of sensors that is sufficient for performing assigned tasks. The exact definition depends on the task or the particular desirable properties of a backbone. We discuss two specific kinds of backbones, neighbor and area dominating sets, that we believe are the essential and perhaps only backbones required for sensor networks. A sensor is covered by a backbone if it is in the backbone or is a neighbor to a sensor in the backbone. This type of backbone is referred to here as neighbor-dominating sets, or simply dominating sets. A point within a monitoring area is covered by a sensor backbone if it is within sensing range of at least one sensor from the backbone. This type of backbone is called area-dominating set. In a broadcasting (also known as data-dissemination) task, a message is sent from one node, which could be a monitoring center, to all nodes in the network. Sensors, which are randomly placed in an area, decide which of them should be active and monitor an area, and which of them may sleep and become active at a later time. The communication connectivity is important so that the measured data can be reported to a monitoring center. This problem is known as the sensor-area coverage problem, and needs to be solved efficiently to enable sensor functioning for a prolonged time. Sensors may also be placed deterministically in an area to optimize coverage and reduce power consumption. Most solutions considered in this chapter are based Handbook of Sensor Networks: Algorithms and Architectures, Edited by I. Stojmenovic ÍSBN 0-471-68472-4